Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-10-29T23:28:20.745Z Has data issue: false hasContentIssue false
  • English
  • Français

TRANSIENT ANALYSIS OF IMMIGRATION BIRTH–DEATH PROCESSES WITH TOTAL CATASTROPHES

Published online by Cambridge University Press:  07 January 2003

Xiuli Chao  and
Yuxi Zheng
Xiuli Chao
Affiliation:
Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, E-mail: xchao@unity.ncsu.edu
Yuxi Zheng
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, E-mail: yzheng@math.psu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 1 , January 2003 , pp. 83 - 106
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable